Mariss Jansons has had health problems since at least 1996, when he nearly died from a heart attack on stage. Photograph: David Levene

The chief conductor of Amsterdam's Royal Concertgebouw Orchestra, Mariss Jansons, is to step down after leading the world-famous ensemble for a decade.

The RCO announced on Tuesday that the celebrated conductor will retire at the end of the 2015 season from what is widely considered to be one of the greatest posts in the orchestral world.

The news of his departure came as a surprise even to those in his orchestra, despite health concerns. In April 1996, Latvian-born Jansons nearly died on stage in Oslo from a heart attack while conducting the final pages of Puccini's La Bohème. An official at the RCO said: "It's no secret that he has health problems."

The exact date of the 71-year-old's last performance has not been determined, the RCO said, adding: "The orchestra, management and the chief conductor want to make a point of stating that they are parting on excellent terms and with deep mutual respect."

It said: "Mariss Jansons has always been able to inspire the orchestra and lead it in great performances. Due to his knowledge, commitment and involvement, he is much loved by both musicians and his audiences."

The son of a conductor, Jansons studied violin in St Petersburg before travelling to Vienna and Salzburg to learn under the internationally renowned conductors, Hans Swarowsky and Herbert von Karajan.

He went on to conduct the BBC Welsh Symphony orchestra before becoming chief conductor at the RCO in 2004.

Musicians and classical critics played tribute to Jansons's long and eminent career as a conductor.

Dominic Seldis, the RCO's principal double bass player, said Jansons was "more dedicated than anybody I've ever worked with" and he would miss him terribly.

"Mariss pushes himself so incredibly hard and he worked fifty times harder than all of us put together," said Seldis. "Yes, news of his departure was a surprise but in a way it's a relief because his health has not been getting any better."

He continued: "We will all remember him for his detail, passion and immense musicality and knowledge. He is the don. There is nothing in every score he conducts that he hasn't read, researched, discussed, thought about and worried about.

"Working with him, the depth of knowledge and musicality is amazing. It was a complete and utter privilege to have worked with him and it is even more of a privilege to call him a friend. I will miss him but I'm delighted that he has finished on a high that is fitting to both a great conductor and a great man."

Seldis said that while Jansons's replacement still remained unknown, he believed the RCO was ready for the next chapter.

"The orchestra is on great form," he added. "We've had the most unbelievable year, with our 125th anniversary, so we are now just looking forward to whoever steps up."

Jansons was appointed assistant to the conductor Yevgeny Mravinsky of the Leningrad Philharmonic Orchestra in 1973. From 1979 to 2000 he was chief conductor at the Oslo Philharmonic Orchestra.

The classical critic Geoffrey Norris described Jansons as "one of the greatest conductors of his generation" and praised his inspiring and humanising touch.

"Jansons always said that he likes his performances to be cosmic and I think when he's at his best, this is what you get," said Norris. "You find yourself completely transported by his musicianship and the way he can inspire orchestras to achieve their absolute best."

He added: "I've been following Jansons since the 1980s when he was conductor of the BBC Welsh Symphony Orchestra. He cut his teeth there and I remember even in those days you felt that you were listening to a musician of extraordinary ability who could really transform you as you listened.

"He has a very rare ability to communicate his ideas to orchestras and inspire them in their music making."

Nicholas Kenyon, the managing director of the Barbican, which hosted the RCO in 2012, also paid tribute.

"The partnership between Mariss Jansons and the Concertgebouw has been one of the world's great musical relationships over the last decade and they have just given us three unforgettable Bruckner symphonies at the Barbican," he said.

"It's of course a huge pity that will be coming to an end next year and I hope Mariss will continue giving us his peerless music-making for many years to come."

Jansons will continue in his post as chief conductor of the Bavarian Radio Symphony Orchestra in Munich, where his contract lasts until 2018.